Question

In a dog show, there will be a gold and silver medal awarded.There are 6 finalists. In how many ways can the 2 medals be awarded

Answer 1

Answer:

30

Step-by-step explanation:

Given: There are six finalists and two medals. That is it asks for the possibilities of 6 finalists taking two at a time. Say, for example the first and third finalist or the second and the sixth finalist and so on. The number of possibilities is given by $^nP_r$

                       $^nP_r = \frac{n!}{(n - r)!}$

So the number of possibilities of 6 finalists taken two at a time is $^6P_2$

$\implies \frac{6!}{(6 - 2)!} = \frac{6!}{4!} \hspace{15mm} [n! = n \times (n-1) \times (n - 2) \times . . . 2 \times 1]$

$\implies \frac{6 \times 5 \times 4 \times \times 3 \times 2 \times 1}{4 \times 3 \times 2 \times 1} = 6 \times 5 = 30$